Electrical Machines (EELE 3351)

Site.iugaza.edu.ps/ajasser Assad Abu-Jasser, PhD Electric Power Engineering The Islamic University of Gaza ajasser@iugaza.edu.ps Site.iugaza.edu.ps/ajasser

Chapter 1 Introduction To Machinery Principles

Angular Position, Velocity and Acceleration θ angle at which it is oriented, radians/degrees +ve anticlockwise rotation -ve clockwise rotation

Torque, Work and Power

Newton’s Law of Rotation  - Torque J - moment of inertia - angular acceleration F - Force applied m - mass of object a - acceleration of object

The Magnetic Field Production of a Magnetic Field

Magnetic Circuits

Example 1.1 A ferromagnetic core is shown. Three sides of this core are of uniform width, while the fourth side is somewhat thinner. The depth of the core (into the page) is 10cm, and the other dimensions are shown in the figure. There is a 200 turn coil wrapped around the left side of the core. Assuming relative permeability µr of 2500, how much flux will be produced by a 1 A input current?

Example 1.2 Figure shows a ferromagnetic core whose mean path length is 40cm. There is a small gap of 0.05cm in the structure of the otherwise whole core. The csa of the core is 12cm2, the relative permeability of the core is 4000, and the coil of wire on the core has 400 turns. Assume that fringing in the air gap increases the effective csa of the gap by 5%. Given this information, find (a) the total reluctance of the flux path (iron plus air gap) (b) the current required to produce a flux density of 0.5T in the air gap.

Example 1.3 Figure shows a simplified rotor and stator for a dc motor. The mean path length of the stator is 50cm, and its csa is 12cm2. The mean path length of the rotor is 5 cm, and its csa also may be assumed to be 12cm2. Each air gap between the rotor and the stator is 0.05cm wide, and the csa of each air gap (including fringing) is 14cm2. The iron of the core has a relative permeability of 2000, and there are 200 turns of wire on the core. If the current in the wire is adjusted to be 1A, what will the resulting flux density in the air gaps be?

Ferromagnetic Materials Behavior

Example 1.4 Find the relative permeability of the typical ferromagnetic material whose magnetization curve is shown at (a) H=50, (b) H=100, (c) H=500, and (d) H=1000 A-turn/m.

Example 1.5 A square magnetic core has a mean path length of 55cm and a csa of 150cm2. A 200 turn coil of wire is wrapped around one leg of the core. The core is made of a material having the magnetization curve shown below. Find: (a) How much current is required to produce 0.012 Wb of flux in the core?, (b) What is the core’s relative permeability at that current level?, and (c) What is its reluctance?

Ferromagnetic Core Losses Hysteresis and Eddy Losses DC Excitation

Faraday’s Law of Induction Time-varying Magnetic Field If a flux passes through a turn of a coil of wire, voltage will be induced in the turn of the wire that is directly proportional to the rate of change in the flux with respect of time (Faraday’s Law) Video Animation https://www.youtube.com/watch?v=tC6E9J925pY The direction of the build-up voltage in the coil is as such that if the coils were short circuited, it would produce current that would cause a flux opposing the original flux change (Lenz’s Law)

Example 1.6 The coil of wire wrapped around the iron core in the figure shown has 100 turns. If the flux in the core is given by Φ=0.05 sin 377t Wb. Determine the voltage induced at the terminals of the coil and its polarity when flux is increasing in the reference direction shown.

Induced Force on a Wire Left Hand rule Video Animation https://www.youtube.com/watch?v=HYPfjU2tBG4

Induced Force on a Wire Right Hand rule θ angle between conductor and magnetic field

Example 1.7 The figure shows a wire carrying a current in the presence of a magnetic field. The magnetic flux density is 0.25T, directed into the page. If the wire is 1m long and carries 0.5A of current in the direction from the top of the page to the bottom, what are the magnitude and direction of the force induced on the wire?

Induced Voltage on a Conductor Moving in Magnetic Field

Example 1.8 The figure shows a conductor moving with a velocity of 5m/s to the right in the presence of a magnetic field. The flux density is 0.5T into the page, and the wire is 1m length, oriented as shown. What are the magnitude and polarity of the resulting induced voltage?

Example 1.9 Figure shows a conductor moving with a velocity of 10m/s to the right in a magnetic field. The flux density is 0.5T, out of the page, and the wire is 1m in length. What are the magnitude and polarity of the resulting induced voltage?

End Of Chapter One